Pith Number

pith:LRFRNUPK

pith:1999:LRFRNUPKPSUYYC4FXYVPUTXEKG

not attested not anchored not stored refs pending

Percolation and number of phases in the 2D Ising model

H.-O. Georgii, Y. Higuchi

arxiv:math/9907186 v3 · 1999-07-29 · math.PR · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LRFRNUPKPSUYYC4FXYVPUTXEKG}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T01:38:22.440879Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5c4b16d1ea7ca98c0b85be2afa4ee45198b262721ba7b789a0e2900bfaeaf621

Aliases

arxiv: math/9907186 · arxiv_version: math/9907186v3 · doi: 10.48550/arxiv.math/9907186 · pith_short_12: LRFRNUPKPSUY · pith_short_16: LRFRNUPKPSUYYC4F · pith_short_8: LRFRNUPK

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LRFRNUPKPSUYYC4FXYVPUTXEKG \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 5c4b16d1ea7ca98c0b85be2afa4ee45198b262721ba7b789a0e2900bfaeaf621

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b42a3edcc90f2627e579e2ceed62e16eb2c48c44ade8009f4ca216f14756bff",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "1999-07-29T16:09:46Z",
    "title_canon_sha256": "9e4b1f4fd862a5564f030068f92cac548a09e6e19a1da24339b52bc1512fabce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9907186",
    "kind": "arxiv",
    "version": 3
  }
}